Download Review of Work and Energy

Review of Work and Energy
Work is the process that changes energy from one form to another or one place to another. For work to be
done, a force must act on an object, and the position of the object must change. The force must be
responsible for the transfer of energy.
for constant forces:

for variable forces:
for any force:
W = Force · displacement
W=
W = (F) (r) cos 
∫ F(r) · dr
W = the area “under” a Force vs position graph
Mechanical energy consists of kinetic energy (dependent on mass and speed), elastic potential energy
(dependent on the spring constant and amount of deformation) and gravitational potential energy
(dependent on weight and height).
K = ½ m v2
Us = ½ kx2
Ug = mgh
F = -dU/dx
Mechanical energy of an object is changed if work is done on the object by a non–conservative force. Two
conservative forces: the gravitational force, and the restoring (spring) force.
Fs = -kx
Fg = mg
The work done by non-conservative (or external) forces can be calculated in the way one calculates the
work done by any individual force, as shown above, or using the work – energy equation:
U + K + WNC = U + K
When kinetic friction or drag does work, mechanical energy is converted into heat energy. When any other
non-conservative force does work, energy is converted from some form into mechanical energy if W NC is
positive, and energy is converted from mechanical to some other form (usually heat) if W NC is negative.
Power is defined as the rate at which work is done.
P = W÷t
P = dW / dt
P=Fv